On the Capacity Bounds of Undirected Networks

TL;DR

This paper refines capacity bounds for undirected networks, demonstrating that routing can achieve significant throughput and that coding gain remains below 2, with bounds depending on the number of terminals.

Contribution

It provides improved bounds on network coding gain for undirected networks, including a tight bound for three terminals and a general bound approaching 2 for many terminals.

Findings

Routing achieves at least 75% of coding throughput with fractional routing.

Coding gain is strictly less than 2 for any number of terminals.

Bounds depend on the number of terminals and approach 2 as terminals increase.

Abstract

In this work we improve on the bounds presented by Li&Li for network coding gain in the undirected case. A tightened bound for the undirected multicast problem with three terminals is derived. An interesting result shows that with fractional routing, routing throughput can achieve at least 75% of the coding throughput. A tighter bound for the general multicast problem with any number of terminals shows that coding gain is strictly less than 2. Our derived bound depends on the number of terminals in the multicast network and approaches 2 for arbitrarily large number of terminals.